System and method of multi-dimensional force sensing for scanning probe microscopy

ABSTRACT

A SYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR SCANNING PROBE MICROSCOPY is provided.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] Under 35 U.S.C. §120, this application claims the benefit of commonly owned U.S. patent application Ser. No. 09/499,101 entitled SYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Feb. 4, 2000, which is also hereby incorporated by reference.

[0002] Additionally, via U.S. patent application Ser. No. 09/499,101, and under 35 U.S.C. §119(e) and 120 and 37 C.F.R. § 1.53(b), this application further claims the benefit of commonly owned U.S. Provisional Patent Application No. 60/118,756 entitled MULTIDIMENSIONAL FORCE SENSING SYSTEM FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Feb. 5, 1999, which is also hereby incorporated by reference.

[0003] This application also incorporates by reference commonly owned U.S. patent application Ser. No. 09/404,880 entitled MULTI-DIMENSIONAL SENSING SYSTEM FOR ATOM FORCE MICROSCOPY, by Vladimir Mancevski, hereinafter referred to as “MANCEVSKI1.”

[0004] Furthermore, this application also incorporates by reference commonly owned issued U.S. Pat. No. 6,146,227 entitled METHOD FOR MANUFACTURING CARBON NANOLOBES As FUNCTIONAL ELEMENTS OF MEMS DEVICES, by Vladimir Mancevski, hereinafter “MANCEVSKI2.”

TECHNICAL FIELD OF THE INVENTION

[0005] The present invention relates generally to the field of force measurement using scanning probe microscopy (SPM) and, more particularly, to a force measurement system for determining the topography or composition of a local region of interest by means of scanning probe microscopy.

BACKGROUND OF THE INVENTION

[0006] Introduction of Terms Used in this Disclosure

[0007] In this invention we use Cartesian coordinate systems with perpendicular axes as the coordiante system of choice. Nevertheless, one may implement any other well-defined coordinate system including, for example, polar, cylindrical, or spherical coordinate system. The “global” coordinate system X Y Z is fixed with the sample and the “local” coordinate system X_(tip) Y_(tip) Z_(tip) is fixed with the scanning probe tip apex. In general, the scanning probe tip apex may have an arbitrary position and orientation with respect to the sample, therefore, the local coordinate system also may have arbitrary position and orientation with respect to the global coordinate system, as shown in FIG. 1A. In a special case, the local and global coordinate systems may be aligned with respect to one another, as shown in FIG. 1B.

[0008] The origin of the local coordinate system is at the apex of the tip. The Z_(tip) axis is oriented along the length of the tip and is perpendicular to a region of the oscillator surface near the place where the tip is attached. The X_(tip) axis is parallel to the long axis of the oscillator. The Y_(tip) axis is transverse with respect to the X_(tip) so as to form a right-handed Cartesian coordinate system.

[0009] It is known that a dipole-dipole interaction occurs between pairs of atoms located in volumetric regions of the tip and sample when they are in proximity to each other. The associated force is called Van der Walls force. The resulting integrated effect encompasses all dipole-dipole interactions between pairs of atoms in sufficient proximity to generate a measurable interaction between the tip and the sample. This resultant of the integrated dipole-dipole interaction is represented by a three-dimensional “tip-sample interaction force vector” as shown in FIG. 2A. A single point can be used to approximate the volumetric region near the tip apex, and a flat surface can be used to approximate the region of the sample in proximity to the tip, as shown in FIG. 2B. If the sample surface is horizontal (i.e., in the XY plane) the tip-sample interaction force vector will be vertical. However, if the surface is vertical (e.g., in the XZ plane) the tip-sample interaction force vector will be horizontal. For a general orientation of the surface, the tip-sample interaction force vector will have three non-zero components, corresponding to the three axes XYZ of the global coordinate system. The tip-sample interaction force vector F can be represented either by its components F_(x tip), F_(y tip), F_(z tip) in the local coordinate system or by its components F_(X), F_(Y), F_(Z), in the global coordinate system.

[0010] A single point can be used to approximate the volumetric region near the tip apex, and a flat surface can be used to approximate the region of the sample in proximity to the tip, as shown in FIG. 2B. If the sample surface is horizontal (i.e., in the XY plane) the tip-sample interaction force vector will be vertical. However, if the surface is vertical (e.g., in the XZ plane) the tip-sample interaction force vector will be horizontal. For a general orientation of the surface, the tip-sample interaction force vector will have three non-zero components, corresponding to the three axes XYZ of the global coordinate system.

[0011] In one possible mathematical representation, the 3×1 vector functions Φ_(i), for (i=1, 2, 3, . . . ∞), of the spatial coordinates (e.g., X_(tip) Y_(tip) Z_(tip)) represent mode shapes of the probe structure, and q_(i) represent the corresponding generalized coordinates. In one instance of a classical modal analysis, the equations of motion of the probe are

M _(j) d ² q _(j) /dt ² +M _(j)ω_(j) ² q _(j)−Σ_(i=1 to ∞) F _(ij) ′q _(i) =F _(0j)

[0012] where (j=1, 2, 3, . . . ∞), M_(j) is the modal mass, ω_(j) is the resonant frequency, and F_(0j) is the static component of the generalized force corresponding to the tip-sample interaction force applied to the probe tip. The term—Σ_(i=1 to ∞) F_(ij)′ q_(i) can be interpreted as a negative spring force which alters the j^(th) resonant frequency of the vibrating probe. The quantity F_(ij)′ can be represented in terms of the mode shapes by

F _(ij) ′=[A]Φ _(i)(tip)·Φ_(j)(tip)

[0013] Where [A] is a 3×3 coefficient matrix arising from classical modal analysis and the symbol · denotes an inner product of two vectors.

[0014] The vector [A] Φ_(i) (tip), derived from classical modal analysis, is an example of a more general vector quantity that we call a “resultant surface force interaction.” Our use of the term “resultant surface force interaction” is not limited to any particular physical origin of the tip-sample interaction force and may include, for example, both conservative and non-conservative tip-sample interaction forces.

[0015]FIG. 3A shows typical orientations of three selected mode shape vectors, evaluated at spatial coordinates corresponding to the apex of a probe tip. In this example, Φ₁ (tip) represents the direction in which the tip apex moves when the main bending mode is excited, Φ₂ (tip) represents the direction in which the tip apex moves when the first torsional mode is excited and Φ₃ (tip) represents the direction in which the tip apex moves when the second bending mode is excited. For a suitably chosen structural design of the probe and tip apex location, and for small-amplitude vibrations, Φ₃ (tip), Φ₂ (tip) and Φ₁ (tip) are nearly aligned with the unit vectors, i_(tip), j_(tip), k_(tip) and the modal coordinates q₃, q₂, q₁ can be approximated by tip displacements along the in the X_(tip) Y_(tip) Z_(tip) axes respectively. In this example the resultants of the surface force interaction can be given a geometric interpretation as vectors aligned along the X_(tip) Y_(tip) Z_(tip) axes.

[0016] The resultant surface force interaction vectors F′_(x tip), F′_(y tip) and F′_(z tip) can, in some cases, be modeled by the three virtual springs with variable spring constants k₁, k₂, and k₃ that are functions of the tip-surface distance, as shown in FIG. 3B. The vector F′ shown in FIG. 3C is the sum of the three resultant surface force interaction vectors. As shown in FIGS. 4A and 4B, the resultant surface force is non-linear with respect to the tip-surface distance. Therefore, the modeled spring constants are also non-linear. However, for small amplitudes of vibration of the oscillator tip, the spring constants are linear with respect to the tip-surface distance. To maintain linear response, the oscillator should vibrate with sufficiently small amplitude to keep the oscillator in a linear regime of operation.

[0017] The term “oscillator,” as used in conjunction with the present invention, represents a scanning probe for which multiple resonant modes are intended to be used for force sensing. The term “cantilever” refers to a scanning probe for which only the primary bending (i.e., “cantilever”) mode is intended to be used for force sensing, even though, in general, the probe structure would exhibit multiple resonant modal responses if excited at the appropriate driving frequencies.

[0018] The term “force sensor” refers to the resonating oscillator and its sensitivity to surface forces associated with the tip-sample interactions. The purpose of the force sensor is to enable detection of the surface topology or composition by means of coupling the scanning probe tip to the surface of the sample via a tip-sample interaction force. In general, the interaction force between the tip and the sample is a non-linear function of the tip-surface gap that includes the dipole-dipole interaction described above (which is conservative and hence describable by a potential), plus additional contributions from other conservative forces (e.g. electrostatic and magnetic forces) and non-conservative forces (e.g., meniscus forces and other forces due to surface contamination). However, whatever its origin in terms of atomic interactions, molecular interactions or other surface physics phenomena, the tip-sample interaction force vector can still be represented by a vector composed of three generally non-zero components, corresponding to the three axes XYZ of the global coordinate system. Alternatively, the tip-sample interaction force can be represented by a vector composed of three generally non-zero components, corresponding to the three axes X_(tip) Y_(tip) Z_(tip) of the local coordinate system. Equal and opposite tip-sample interaction forces act on the tip and sample, respectively, consistent with Newton's law of action and reaction.

[0019] “Force sensing” occurs when the surface force interaction alters the effective elastic restoring force associated with one or more resonant modes of the primary probe structure so as to shift the respective natural frequencies of its resonant modes. The shifts in natural frequency can be sensed, for example, by monitoring either the amplitudes or phases of the respective modal oscillations.

[0020] Background of the Related Art

[0021] A scanning probe typically consists of a primary probe structure, (which may be either an oscillator or a cantilever) and a high aspect-ratio, sharply-pointed tip extending from its end. The tip is generally much less massive than the primary probe structure. The function of the primary probe structure is to provide one resonant mode (in the case of a cantilever) or more than one resonant mode (in the case of an oscillator) which are utilized for force sensing. Typically, the primary probe structure is about 100 microns long by 30 microns wide by 2 microns thick. The function of the tip is to rigidly couple the primary probe structure to a relatively small volumetric region (the tip apex) which can be positioned so as to interact with a relatively small region of the sample in proximity to the tip apex. Typically, the tip is an inverted cone or a pyramid with its apex pointing towards the sample surface. Ideally, the apex of the tip would be a single atom that couples with the sample surface via the tip-sample force interaction. In reality, the apex of the tip typically has a radius of about 10 nanometers, and the cone-shaped or pyramid-shaped tip is typically a few microns long.

[0022] In conventional scanning probe microscopy (SPM), the force sensor is only sensitive to the resultant of the surface force interaction F′_(Z tip), in the Z_(tip) direction, as illustrated in FIGS. 5A and 5B. The other two components of the surface force interaction vector, F′_(X tip) in X_(tip) direction and F′_(Y tip) in the Y_(tip) direction, are not detected in conventional scanning probe microscopy. The XYZ and X_(tip) Y_(tip) Z_(tip) coordinate systems are shown in FIGS. 5A and 5B as being aligned for ease of illustration. For conventional non-contact mode scanning, a SPM cantilever is excited in its first bending mode with small amplitude, thereby causing the tip to move within the attractive region of the surface force interaction profile. This region is illustrated in FIG. 4A. In the conventional “tapping” mode, the amplitude of the cantilever vibration is larger and the tip dips in and out of both the attractive and repulsive regions of the surface force interaction region, as shown in FIG. 4B. A change in the tip-surface distance during the scanning process shifts the cantilever resonance. A feedback loop uses the resonance shift to maintain either the amplitude or phase of the oscillation at a predetermined value. The output from the resulting scan is used to represent the topography or composition of the surface. Scanning of the probe in an XY raster plane while recording the response of the force sensor in Z direction can be used to construct a three-dimensional profile of the surface.

[0023] There are two major consequences of the failure of conventional SPMs to detect the surface force interaction in multiple directions: (1) the vertical and horizontal distance scales will be different due to a diminished projection of the surface force interaction vector onto the vertical axis when the sample surface is not horizontal, and (2) there will be loss of force sensor sensitivity over highly sloped sample surfaces. To illustrate these points, we examine a tip that is oriented in the Z direction as it scans in the Y direction over a horizontal surface in the XY plane, as shown in FIG. 6. In this scenario, the surface force interaction will be in the Z direction when the surface is horizontal. A conventional force sensor would drive the tip at a constant surface force interaction set for scanning the horizontal surface. If the slope of the surface changes, and with that the direction of the surface force interaction vector, the conventional force sensor would still only respond to the surface force interaction in the Z direction. However, for a tilted surface, the surface force interaction in the Z direction is diminished by a factor equal to the cosine of the surface slope angle. The feedback controller of the conventional force sensor would keep the tip over the sloped surface at a constant surface force interaction level set for the horizontal surface. This misrepresentation will cause the tip to be closer to a sloped surface than to a horizontal surface, causing a distortion of the horizontal and vertical distance scales and a distortion of the surface topography. This unwanted approach of the tip to the surface may also cause snapping of the tip to the surface. This snapping may damage the tip or the sample.

[0024] Naturally, this problem is more emphasized when the surface is close to vertical or is vertical. For the case of a vertical surface, the surface force interaction occurs only in the horizontal direction. However, the conventional force sensor is only sensitive to a surface force interaction in the vertical direction. Therefore, the conventional force sensor loses its sensitivity over highly sloped surfaces and would not work for vertical or close to vertical surfaces.

[0025] One prior art embodiment, shown in FIG. 7, operates in a non-contact mode and has a cantilever that resonates in the Z direction and dithers (a non-resonant vibration) in the Y direction. This approach is sufficient to enable force sensitivity in two directions. However, the force sensitivity in the lateral direction is not as good as the force sensitivity in the vertical direction. This is due to the use of dithering in the Y direction rather than use of a distinct resonant mode that can provide higher force sensitivity. If the sample surface is vertical, the vertical surface force interaction vanishes completely which renders the dithering approach ineffective.

[0026] Therefore it would be desirable to operate a force sensor that provides force sensitivity in all three directions by means of distinct resonant modes.

[0027] All references cited herein are incorporated by reference to the maximum extent allowable by law. To the extent a reference may not be fully incorporated herein, it is incorporated by reference for background purposes, and indicative of the knowledge of one of ordinary skill in the art.

BRIEF SUMMARY OF THE INVENTION

[0028] The problems and needs outlined above are largely solved and met by the present invention. In accordance with one aspect of the present invention, a scanning probe microscopy (SPM) tool is provided. The SPM tool comprises an oscillator, an SPM tip, a mechanical actuator, a sensing system, and a feedback control system. The oscillator having the SPM tip extending therefrom. The mechanical actuator is adapted to hold the oscillator and position the SPM tip relative to a sample. The oscillator has a selected shape, dimensions ratio, and/or material composition such that the oscillator comprises a first resonant mode for a first direction, wherein a first resonance of the first resonant mode can be altered by a surface force interaction between the SPM tip and the sample in the first direction; and a second resonant mode for a second direction, wherein a second resonance of the second resonant mode can be altered by the surface force interaction between the SPM tip and the sample in the second direction. The sensing system is adapted to sense the alterations in the first and second resonances, and being adapted to provide a first output based on the alterations in the first resonance, and being adapted to provide a second output based on the alterations in the second resonance. The feedback control system is adapted to control the actuator based on the first and second outputs. Nanotubes can be grown from the tip to provide more advantages.

[0029] In accordance with another aspect of the present invention a multidimensional force sensor system for use in scanning probe microscopy is provided, which comprises:

[0030] an oscillator having a rigid pointed tip extending therefrom, the oscillator having a means for being sensitive to surface force interactions between the tip and a sample surface in a first direction with a first resonance frequency, in a second direction with a second resonance frequency, and in a third direction with a third resonance frequency;

[0031] a means for holding the probe structure and for positioning the tip and the sample relative to each other;

[0032] a means for vibrating the probe structure at the first, second, and third resonance frequencies;

[0033] a means for sensing the surface force interactions in the first, second, and third directions;

[0034] a means for providing a first output based on the surface force interactions in the first direction;

[0035] a means for providing a second output based on the surface force interactions in the second direction;

[0036] a means for providing a third output based on the surface force interactions in the third direction; and

[0037] a means for controlling the actuator based on the first, second, and third outputs.

[0038] Also, one or more nanotubes can be grown onto the tip to provide other embodiments and more advantages. The means for mentioned are detailed in the other portions of this specification. Other aspects and embodiments of the present invention will be described in the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings in which like reference numerals indicate like features and wherein:

[0040]FIG. 1A shows scanning probe tip with an arbitrary position and orientation with respect to the sample;

[0041]FIG. 1B shows a special case of FIG. 1A in which the local and global coordinate systems are aligned with respect to one another;

[0042]FIG. 2A shows the tip-sample interaction force vector as the resultant of the integrated dipole-dipole interaction;

[0043]FIG. 2B shows a single point used to approximate the volumetric region near the tip apex, and shows a flat surface used to approximate the region of the sample in proximity to the tip;

[0044]FIG. 3A shows typical orientations of three selected mode shape vectors, evaluated at spatial coordinates corresponding to the apex of a probe tip;

[0045]FIG. 3B shows the resultant surface force interaction vectors modeled by the three virtual springs with variable spring constants that are functions of the tip-surface distance;

[0046]FIGS. 4A and 4B show the resultant surface force as a non-linear function with respect to the tip-surface distance;

[0047]FIGS. 5A and 5B show that in conventional scanning probe microscopy (SPM), the force sensor is only sensitive to the resultant of the surface force interaction in the direction along the length of the tip;

[0048]FIG. 6 shows scale error that occur when a tip f a conventional SPM that is oriented in the Z direction scans over a sloped surface;

[0049]FIG. 7 shows a prior art embodiment has a cantilever that resonates in the Z direction and dithers (a non-resonant vibration) in the Y direction;

[0050]FIG. 8 shows the first bending mode which generates tip vibration in the direction along the length of the tip;

[0051]FIG. 9 shows the first torsional mode which generates tip vibration in the direction transverse to the long axis of the oscillator;

[0052]FIG. 10 shows the second bending mode which generates tip vibration in the direction along the long axis of the oscillator;

[0053]FIG. 11 shows a scanning probe tip located at a node of a mode shape;

[0054]FIG. 12 shows another embodiment of the present innovation that utilizes paddle-shaped oscillator made of single crystal silicon;

[0055]FIG. 13 shows another embodiment of the present innovation that utilizes notched diving-board shaped oscillator;

[0056]FIG. 14 shows the spatial domain based method of vibration sensing;

[0057]FIG. 15 shows alterations of multiple resonances in response to tip-surface interactions in multiple directions. FIG. 15 also shows the directions of tip motion for the first bending and first torsional modes of the oscillator;

[0058]FIG. 16 shows an embodiment of the present invention where the oscillator is tilted around the long axis of the oscillator to provide access to a feature with reentrant sidewall;

[0059]FIG. 17 shows a SPM tip reaching vertical and reentrant sidewall surfaces of a sample with periodic dense high-aspect-ratio features;

[0060]FIG. 18 shows an experimentally obtained scan of a line in a semiconductor integrated circuit with the tilted probe system;

[0061]FIG. 19 shows an embodiment of the present invention in which standard oscillator tip is extended with an aligned nanotube tip grown from the apex of the sharp tip using the method of MANCEVSKI2;

[0062]FIG. 20 shows an embodiment of the present invention with a support structure on which carbon nanotube tip extensions are oriented in lateral and vertical directions as to enable imaging of vertical and near vertical sidewalls and trench bottoms; carbon nanotube tip extensions may also function as nanotube oscillators;

[0063]FIG. 21 shows three possible resonant modes of a carbon nanotube oscillator; and

[0064]FIG. 22 shows a magnetic particle attached at the end of the nanotube so as to destroy the symmetry and produce distinct resonances with separated modes; the magnetic particle may also be used to magnetically excite the nanotube oscillator.

DETAILED DESCRIPTION OF THE INVENTION

[0065] Referring now to the drawings, wherein like reference numbers are used herein to designate like elements throughout the various views, embodiments of the present invention are illustrated and described, and other possible embodiments of the present invention are described. The figures are not necessarily drawn to scale, and in some instances the drawings have been exaggerated and/or simplified in places for illustrative purposes only. One of ordinary skill in the art will appreciate the many possible applications and variations of the present invention based on the following examples of possible embodiments of the present invention.

[0066] System and Method for Force Sensing with Sensitivity in Multiple Directions

[0067] The system and method for force sensing of the present invention relies on the use of three separate oscillator resonant modes to become sensitive in three directions, where the modal shape of the oscillator and the location of the tip apex determine the direction of the force sensor sensitivity.

[0068] A particular resonant shape and particular tip apex location in a proximity to a three-dimensional surface will result in a surface force interaction that will act only in the direction of the tip vibration altering the given resonance. For that particular resonant mode, the actual surface force interaction will not produce any work in any other axis but the axis of the vibration of the tip.

[0069] Ideally, each oscillator resonant mode corresponds to a single direction of the force sensor sensitivity. However, each oscillator resonant mode may correspond to multiple (two or three) directions of the force sensor sensitivity. Preferably, the three directions are different from each other. Preferably, the three directions are perpendicular to each other. Preferably, the three perpendicular directions are aligned with the X_(tip), Y_(tip), and Z_(tip) axis of the oscillator.

[0070] For a given relative position and orientation between the local coordinate system of the scanning probe and a global coordinate system of the sample surface we can transform the directions of the force sensor sensitivity to any coordinate system of choice. Preferably, the coordinate system of choice is the global coordinate system of the sample.

[0071] A second embodiment of the present invention relies on the use of at least two separate oscillator resonant modes to become sensitive in at least two (preferably Y_(tip) and Z_(tip)) directions.

[0072] Advantages of the Present Invention

[0073] The present invention provides a force sensor that overcomes the limitations of the conventional force sensors described in the background section of this disclosure.

[0074] The force sensor of the present invention provides an important technical advantage by providing sensitivity in three directions, in contrast to the conventional force sensor that is only sensitive to one direction.

[0075] The advantage of the force sensor of the present invention is that it can determine the vertical and horizontal dimensions with equal distance scales irrespective of the slope of the sample surface. Additionally, the force sensor of this invention is capable of scanning over horizontal, near vertical, vertical, reentrant and other arbitrarily sloped surfaces. This makes scanning possible on complex surfaces with curvatures, edges, corners, and undercuts, all of them in three-dimensional space. The advanced capabilities of the force sensor of this invention make it very suitable for high precision measurements required for metrology applications. In particular the invention is applicable for critical dimension measurements of semiconductor integrated circuits.

[0076] Multiresonant Oscillators

[0077] The key to the functioning of the present invention is the use of a multiresonant oscillator with three separate oscillator resonant modes that enable force sensitivity in three directions.

[0078] The resonant modal shapes and a location of the tip will define the directions in which the oscillator is sensitive to surface force interactions. This establishes the design criteria for the multiresonant oscillator.

[0079] It is desirable to design an oscillator that has distinct resonant modes that generate time-varying tip displacement in three orthogonal directions, making each resonance primarily sensitive in only one orthogonal direction.

[0080] The oscillator should have at three distinct resonant modes, where each resonant mode is ideally sensitive to surface force interactions in only one of the orthogonal direction(main effect) and is independent of surface force interactions in the other two orthogonal directions (cross-coupling effect). Some cross-coupling effect can be tolerated. In case of a cross-coupling effect a carefully designed experiment can empirically determine the relationship, or cross-coupling, between the resonances and the surface force interactions in the three orthogonal directions. Furthermore, if the cross-coupling effect is at least an order of magnitude less than the main effect, the cross-coupling may be neglected. Otherwise, the feedback control system needs to compensate for cross-coupling effects.

[0081] It is desirable that the oscillator resonances have a high quality Q factor, that will enable detection of resonance shifts in response to surface force interactions. Failure to detect resonant frequency shifts can cause loss of control and snapping of the oscillator tip to the surface.

[0082] One of the embodiments of this innovation utilizes a simple diving-board shaped oscillator. Three resonant modes that produce three mutually orthogonal vibrations of the tip are, for example, the first bending mode, the first torsional mode, and the second bending mode. The first bending mode generates tip vibrations in the Z_(tip) direction (FIG. 8) and the first torsional mode generates tip vibration in the Y_(tip) direction (FIG. 9). Alternatively, a first lateral bending mode of this oscillator can also be used to generate tip vibration in the Y_(tip) direction. The second bending mode (FIG. 10), can be used to produce tip vibration that is orthogonal to the tip motion produced by the first bending mode and the first torsional mode. The second bending mode generates tip vibrations that are primarily in the X_(tip) direction, and depending on the location of the tip also some small tip vibration in the Z_(tip) direction. This means that the location of the tip with respect to the mode shape determines the degree of mode coupling. If one locates the tip at a node of the mode shape where there is no Z_(tip) displacement, the tip will rock backward and forward along the X_(tip) axis, as shown in FIG. 11. However, if one locates the tip at the end of the oscillator where the displacement is maximum, the tip would experience rocking in the X_(tip) direction as well as displacement in the Z_(tip) direction. In higher order modes it is always possible to find a nodal point that can be used as a strategic point for location of the tip that will decouple one modal displacement from another.

[0083] In general, we are able to use different combinations of distinct resonant modes to produce three mutually orthogonal vibrations of the tip. In addition, we can investigate the modal shapes of any oscillator and determine a location of the tip where three mutually orthogonal tip vibrations exist.

[0084] Naturally, the scanning strategy needs to take advantage of the direction of displacement of the particular modes to make it sensitive in three distinct directions. For example, for the diving-board shaped oscillator excited in first bending and first torsion, the preferred scanning direction is the Y_(tip) direction, laterally with respect to the oscillator. A longitudinal scan in the X_(tip) direction would not take advantage of the direction of the two resonant modes selected for force sensing.

[0085] For more complicated oscillator shapes, the modes selected for force sensing may be quite different than the ones described in the above illustration.

[0086] Another embodiment of this innovation utilizes an oscillator with the shape, size and composition provided in FIG. 12. The probe shown in FIG. 12 is an example of a paddle-shaped oscillator made of single crystal silicon. This oscillator can be excited in resonance modes such as bending, lateral bending, and torsion. In a numerical experiment, the resonances of the oscillator were as follows: Mode Frequency Hz First bending mode  1140 First torsional mode  5509 Second bending mode 11644 Second torsional mode 40194 Third bending mode 55341 Third torsional mode 69500

[0087] This is achieved by selecting the shape and the thickness of the oscillator. The length-to-width ratio of the oscillator contributes to promoting the bending modes. The paddle shape of the oscillator allows excitation of the torsional modes. The thickness of the oscillator can be used to insure that the lateral bending does not occur before the torsional mode. The relevant resonances are dependent upon the overall dimensions of the oscillator (i.e., its length, width and thickness). The resonance frequencies are dependent on {square root}{square root over (m/k)} where k is the modal stiffness and m is the modal mass. Hence, smaller oscillators having less modal mass have higher resonance frequencies. The oscillator depicted in FIG. 12 may have a thickness, t, of approximately 0.15 microns, a width, w, of the paddle of approximately 110 microns, a length, d, of the paddle of 90 microns, and an arm with a width of 20 microns and a length, 1, of 140 microns. These dimensions are used to illustrate one possible embodiment of a paddle-shaped oscillator. However, the present invention need not be limited to this specific set of dimensions or shapes. This paddle-shaped design allows the oscillator to have at three distinct resonant modes.

[0088] Yet another embodiment of this innovation utilizes an oscillator with the shape, size and composition provided in FIG. 13.

[0089] In order that the resonances have a high Q, the oscillator may be manufactured from a single silicon crystal cantilever. Other embodiments may include such materials as silicon nitride or composite layered material. Furthermore, Q is affected by the quality and surface of the oscillator structure.

[0090] Vibration Sensing System

[0091] The function of the vibration sensing system is to transfer the response of the force sensor into information useful for the feedback controller. The feedback controller drives the scanning probe over the sample via three dimensional actuator system.

[0092] The force sensor of this invention has sensitivity in three orthogonal directions, in contrast to the conventional force sensor that is only sensitive to one direction. An embodiment of the present invention uses an oscillator that utilizes resonant modes such as bending, second bending, lateral bending, and torsion, to accomplish force sensing in multiple mutually orthogonal directions. These higher and more complex resonant modes require a greater bandwidth in the vibration sensing system and capability to monitor multiple resonant vibrations simultaneously. The requirement to monitor oscillator vibrations implies that the signal from the force sensor is an AC signal.

[0093] The vibration sensing system needs to be capable of recording the alteration of the multiple resonances under the influence of the surface force interactions.

[0094] In the preferred embodiment of this invention, the vibration sensing system is a laser-bounce based sensing system. In this embodiment there is a focused laser beam pointed towards the oscillator at an oscillator location where there is maximum displacement in all of the resonant modes, and a detector that monitors the displacement of the reflected laser beam. The preferred detector of this invention is a continuous position sensitive detector (CPSD). A CPSD is capable of monitoring the position (DC signal) and displacement (AC signal) of the centroid of the reflected light beam on the surface of its aperture. Alternatively, one may use a quadrant position sensitive detector (QPSD), commonly used with conventional scanning prove tools, to detect the position and displacement of the reflected light beam on the surface of its aperture. However, QPSDs typically require a focusing lens to form perfectly circular reflected light beam on the aperture of the QPSD detector.

[0095] In another embodiment, other types of vibration sensing system are also applicable, such as, a fiber optic or bulk interferometer, an intensity based sensor, light-polarization based sensor, a piezoelectric sensor, capacitive sensor, a magnetometer based sensor, and electromagnetic radiation based sensors. Any of the sensing systems can be an external or integrated with the oscillator. Other types of vibration sensors as known to those with ordinary skills in the art may also be utilized.

[0096] In the present innovation, there are three methods of monitoring the alteration of multiple resonances under the influence of the surface force interactions: (1) in the frequency domain, (2) in the spatial domain, and (3) a combination of the other two methods. The frequency domain method is the preferred vibration monitoring method of this invention.

[0097] In the frequency domain, a single broadband output signal from the detector can be processed with a spectrum analyzer and divided into as many spectral domains as needed. Each of the spectral domains of interest corresponds to each utilized resonant frequency of the oscillator. In the preferred embodiment there are three resonant frequencies of interest. The spectrum analysis can be achieved by notch filtering the detector output signal so as to only allow the frequency of interest to be monitored, by fast-fourier-transformation (FFT) of the detector output signal, and by signal extraction with the help of lock-in amplifier. Since the modal shape of the oscillator determines the direction of the force sensor sensitivity, each frequency already has the information about the direction of the sensitivity already embedded in it. Therefore, the vibration sensing system does not have the responsibility of determining the directions of sensitivity of the force sensor, it only needs to extract information about each frequency of interest.

[0098] In the preferred embodiment, the output of the vibration sensing system includes a vibration amplitude and a phase shift associated with each frequency used for force sensing. A feedback controller utilizes either an amplitude change or phase shift information, or a combination of both to keep the tip at constant surface force interaction levels in all three directions.

[0099] For spatial domain based vibration sensing, we associate each direction of the force sensor sensitivity with a particular spatial displacement of the oscillator or a combination of spatial displacements. In general, spatial displacement of the oscillator may be translational or rotational. The spatial displacements of the oscillator are associated with a direction sensitive detector system that helps transform each direction of the force sensor sensitivity with a unique output that can be used with a feedback controller.

[0100] In the preferred laser-bounce based vibration sensing system of this invention, the direction sensitive detector is a continuous position sensitive detector (CPSD) or a system of strategically positioned CPSDS that help in monitoring the reflected laser beam in spatial displacements that can be geometrically transformed into unique outputs. For a valid geometrical transformation it is important that the number of known CPSD spatial displacements be greater than or equal than the number of unknown spatial displacements of the oscillator to be obtained.

[0101]FIG. 14 illustrates the spatial domain based method of vibration sensing. The system that has an oscillator whose long axis is aligned with the global X coordinate, and a detector aperture that is perpendicular to that axis, in the YZ plane. The incident and reflected laser beams are aligned along the X axis where the incident laser beam is pointed towards the free end of the oscillator at an angle and the reflected laser beam is pointing towards the aperture of the detector and away from the oscillator. In this configuration, a first bending mode of the oscillator would produce a free-end-of-the-oscillator spatial displacement in the Z direction and the reflected laser beam would produce a trace on the detector aperture that extends in the Z direction. A second bending mode of the oscillator would produce free-end-of-the-oscillator spatial displacement mainly in the X direction and the reflected laser beam would produce a trace on the detector aperture that extends in the Z direction. A geometric transformation can be used to decouple the Z output of the detector to determine the contribution from the first and the second bending modes. A first torsion or first lateral bending mode of the oscillator would produce a free-end-of-the-oscillator spatial displacement mainly in the Y direction and the reflected laser beam would produce a trace on the detector aperture that extends in the X direction. A time domain sampling of the laser trace on the aperture of the detector will produce outputs that are associated with the three resonant modes. A geometrical transformation may be used to produce detector outputs that are uniquely associated with the three resonant modes. Therefore, we have obtained three unique detector outputs associated with three resonant modes of the oscillator. Since the modal shape of the oscillator determines the direction of the force sensor sensitivity, we can therefore associate each direction of the force sensor sensitivity with a unique output that can be used with a feedback controller.

[0102] The spatial domain based vibration method allows the present invention to take advantage of multi-dimensional sensing systems, such as those disclosed in MANCEVSKI1, that are capable of sensing angular displacements and vibrations as well as linear displacements and vibrations.

[0103] The multi-dimensional sensing systems described in MANCEVSKIl also disclose an oscillator with a fiducial surface, which is a reflective coating at the free end of the oscillator surrounded by a non-reflective surface. When this mirror-on-an-oscillator is illuminated with a collimated light beam with an illumination area that is many times larger than the area of the fiducial surface, we can observe in-plane displacements and vibrations of the oscillator. Lateral bending mode qualifies as an in-plane motion. Therefore, the oscillator with fiducial surface disclosed in MANCEVSKI1 is suitable for monitoring the lateral spatial displacement of the oscillator displacements of the tip generated with the lateral bending mode.

[0104] In the third vibration sensing system method we combine the frequency domain and spatial domain methods to monitor the vibration signals of the resonating oscillator.

[0105] It is required to that all relevant components of the vibration sensing system, such as the continuous position sensitive detector (CPSD), the associated electronics, the data acquisition, and the control system accommodate the frequency bands of the oscillator resonances. The bandwidth of a typical CPSD sensor disclosed in MANCEVSKI1 is in the MHz region. This frequency band is more than sufficient to be used with most commercially available oscillators. Currently, commercially available PC based data acquisition and control system, such as one from National Instruments, has a bandwidth of 100 KHz for a single channel. A more advanced data acquisition and control system from National Instruments has a bandwidth of 333 to 500 KHz, depending on the digital bit resolution. Those bandwidths are sufficient for implementation of real-time feedback control. However, the present invention need not be limited to this specific PC-based data acquisition and control system. Any data acquisition and control system known to those skilled in the art may be utilized in other embodiments of the present invention.

[0106] In one embodiment of the invention, the output signal from the CPSD is directly digitized with the help of data acquisition hardware. With this approach, the spectral analysis of the signal and the feedback controller may all be done digitally in software. The advantage of this digital approach is its flexibility to handle complex logic operations and sophisticated feedback controllers, and the elimination of expensive analog instruments such as lock-in amplifiers.

[0107] In another embodiment of the present invention the laser intensity of the laser-bounce based vibration sensing system may be time varying instead of being constant. In one embodiment, the frequency of the laser intensity variation may coincide with one or more of the resonant frequencies of the oscillator. In another embodiment, the frequency of the laser intensity variation may be different than the resonant frequencies of the oscillator.

[0108] Excitation System

[0109] The invention also incorporates an excitation system that is used to excite the oscillator resonances used for force sensing. The excitation system of the preferred embodiment uses a piezoelectric (PZT) disk actuator mounted next to the oscillator base to provide mechanical energy to the oscillator. The PZT disk actuator is excited with a signal that is an algebraic sum of signals with frequencies equal or close to the resonant frequencies of the oscillator. The excitation signal will excite only the frequencies of interest and not the other resonant frequencies. The excitation signal is also used as a reference signal for the spectrum analysis of the detector output signal. Other types of oscillator excitation mechanism include electrostatic, magnetic, and thermal.

[0110] Feedback Control

[0111] In principle, the present invention operates by positioning a resonating oscillator with three resonant modes with respect to a three-dimensional surface. Positioning the tip of the oscillator in proximity to the surface alters the excited resonant frequencies of the oscillator. The magnitude of the resonance alteration will depend on the actual distance between the tip and the sample and the orientation between the oscillator and the sample.

[0112] In one embodiment of the present invention the tip-sample distance is controlled by a three-dimensional mechanical actuator. This three-dimensional mechanical actuator moves the tip to a desired distance from the sample surface and in direction consistent with the functioning of our multi directional force sensor. The tip of the oscillator of this invention vibrates with a small amplitude in three perpendicular directions. In the proximity to a sample surface, when a tip is in the attractive atomic force region, a resonance frequency of an oscillator will decrease, and when a tip crosses into a repulsive atomic force region, a resonant frequency of an oscillator will increase. A feedback loop uses the resonance shifts to keep the tip at a constant surface force gradient level in all three directions.

[0113] Several methods can be used to implement the feedback controller. In one method there are three independent PID (proportional-integrated-derivative) controllers, one for each force sensing direction, that operate independently of each other and in a simultaneous manner. These are called three single-input single-output (SISO) controllers. In this method, each controller is not aware of the operation of the other two controllers and any feedback action by the two other controllers will be seen as a disturbance to the third controller. This method works the best when all three resonances are uncoupled and independent. It is possible that once the feedback controllers produce an output to transform the three outputs in another three outputs to satisfy the coordinate system of the actuator.

[0114] In a variation of the SISO controller, each PID controller may be employed one at a time, where some switching logic will be implemented to switch from one controller to another. The switching logic needs to be able to determine when the surface changes direction; for example, an incoming vertical wall after a flat horizontal surface. To satisfy this requirement, one of the resonances that does not participate in the active controlling may be used as a monitor of an incoming surface in the direction in which it is primarily sensitive. After the tip reaches a certain critical point, the PID controllers will be commanded to switch. After such a switch, the resonance that was used for monitoring becomes the primary controlling instrument and the former controlling resonance becomes a monitoring resonance.

[0115] In another method, there are three dependent PID controllers, one for each force sensing direction, that operate coupled with each other and in a simultaneous manner. This implementation uses one multiple-input multiple-output (MIMO) controller. In this method, the column vector of the three inputs from the vibration sensing system is multiplied by a matrix of input-output co-dependencies to produce the actuator output column vector. The matrix represents the cross coupling between the surface force interactions and the resonance alterations associated with the three resonant modes. If there is no cross coupling then the respective off- diagonal matrix elements are zero. For a fully decoupled system the matrix is a diagonal matrix. The coefficients of the matrix may be determined by modeling the force sensor or may be obtained experimentally. For example, one could experimentally observe alterations in resonant frequencies as the oscillator is displaced towards a surface in the X Y and Z directions, respectively.

[0116] In a variation of the MIMO controller, there may be more than three inputs, each associated with an oscillator resonance. Utilizing more than three resonances can improve the confidence level associated with the force sensing. Each of the extra resonances needs to be sensitive to the resultant of the surface force interaction in a particular direction. If an extra resonance is sensitive in more than one direction, the contribution of each surface force interaction of a particular direction to that resonance needs to be known. For example, a second bending mode of our preferred oscillator is mainly sensitive to the resultant surface force interaction in the X_(tip) direction and is somewhat sensitive to the resultant surface force interaction in the Ztip direction. The outputs of this MIMO controller are three actuator signals proportional to the three perpendicular force sensing directions, where each controller output is a result of the contribution of many resonances.

[0117] In a variation of the above MIMO controller, a neural network may be employed to automatically weight the contribution of each surface force interaction of a particular direction to each resonance that we monitor. Neural networks can increase the confidence associated with the force sensing.

[0118] A controller, using any of several different types of control logic, can be used to command actuators to move either the tip or the sample in response to sensed alterations in the natural frequencies of multiple resonances, as shown in FIG. 15. One such type of control logic is to maintain either the amplitudes or phases of the respective resonances at fixed predetermined set-point values, in all three directions. Each direction may have a different set-point. Alternatively, the control logic may include an algorithm for adjusting the amplitude or phase-shift set points associated with the respective resonances during the scan. The amplitude or phase-shift set points can be adjusted either continuously or in discrete steps during the scan. Adjustments of the amplitude or phase-shift set points can be based on an empirically determined control law. Alternatively, adjustments of the amplitude or phase-shift set points can be determined adaptively so as to cause the apex of the tip to move nearly parallel to the sample surface during the scan. Such adaptive adjustments of the amplitude or phase-shift set points require determination and use of a force calibration curve for each of the respective modal resonances used for force sensing. Such force calibration curves relate either the amplitude or phase shift of the respective resonance to the tip-surface distance.

[0119] Improved Scan Control

[0120] In one embodiment, our force sensor can be used to provide additional information useful for improved scan control by building a near real-time estimate of the three-dimensional orientation of the region of the sample surface momentarily in proximity to the tip. This method requires determination and use of a force calibration curve for each of the respective modal oscillations used for force sensing. Such force calibration curves relate either the amplitude or phase shift of the respective oscillation to the tip-surface distance. Surface force interaction vectors along the respective local coordinate axes can be determined once such calibration curves are known. The estimated orientation of sample surface region in proximity to the tip is estimated as normal with respect to the vector F′ shown in FIGS. 3A and 3B (i.e., the sum of the three surface force interaction vectors. This normal assumption is valid for the special case of an infinite homogenous plane sample surface. Other variations of the control logic can be used to take into account the integrated effects associated with a finite, non-planar sample surface. To accomplish improved scan control, the apex of the tip is commanded to move nearly parallel to the estimated sample surface during the scan. This method helps prevent crashing the tip when an abrupt increase of surface slope is encountered (e.g., encountering a vertical wall). This method also helps prevent the tip surface distance from increasing too much when an abrupt decrease in surface slope is encountered (e.g., encountering the edge of a feature).

[0121] In another embodiment, an improved estimate of sample topography can be obtained by post processing the data recorded during a previous scan. Approximate sample topography obtained from the first scan is used to estimate the vector field F′ representing the surface force interactions in the region near the sample surface traversed by the tip during the scan. The scan data is then reprocessed using this new estimate of the vector field F′, resulting in improved estimate of the sample topography. The post processing procedure can be repeated multiple times until differences in estimated surface topography are arbitrarily small. This method allows integrated effects from the surface on the tip to be taken into account. Integrated effects are the cumulative effect of forces from a relevant volume of the sample acting on the tip.

[0122] Other logic systems maybe employed to gather data. For example, one could record a historical surface interaction field F′ based on an SPM tip positioned by the XYZ stage. By retracing the prior motion of SPM tip, one can compare the present surface interaction field to a historical profile. This can be done to verify the repeatability and reliability of scans generated using the present invention. Furthermore, such verifications can be done to provide a quality assurance check on surfaces requiring specific profiles. Another embodiment may use this type of comparison to detect changes or flaws of the surface.

[0123] In yet another embodiment, repeated sampling of a known sample allows the accuracy of the present invention to be improved by tracking the repeatability of the system on a known sample. By sampling a known surface, a new AFM tip can be calibrated by developing a correction factor or matrix that matches the obtained result to the expected result.

[0124] In yet another embodiment of the present invention, the tip can be made to scan longitudinally along narrow features such as metal interconnect lines or resist lines used on the manufacture of semiconductors, instead of laterally with respect to such features. The ability of the present invention to sense a component of the surface force/gradient in the X direction enables such a longitudinal scan. Advantages of scanning such features longitudinally include improved scanning speed and improved ability to measure sidewall roughness.

[0125] Tilted Probe

[0126] In the preferred embodiment of the invention, the oscillator is tilted around the long axis of the oscillator, as shown in FIG. 16. Preferably, the oscillator tilt angle is larger than the half-cone angle of the tip as to allow the apex of the tip to reach vertical and reentrant sidewall surfaces on the sample, as illustrated in FIG. 17. The maximum tilt angle is limited by the width of the oscillator at its free end and the spacing of two sidewall surfaces between which the tip may need to be inserted. In our invention the typical tilt angle is between 6 and 20 degrees but is not limited to this range. In this embodiment, the preferred scan direction is in the Y direction, or laterally with respect to the oscillator. For such a tilted probe, the vertical tip-sample force vector associated with a horizontal sample surface will couple to both the bending and torsional modes of the oscillator, as shown in FIG. 15. Additionally, a horizontal tip-sample force vector associated with a vertical sample surface, will also couple to both the bending and torsional modes of the oscillator, as shown in FIG. 15. Therefore, there will be two surface force components that can be detected by the tilted resonating oscillator in all of its possible angular orientations. Their magnitude will depend on the orientation of the probe tip with respect to the surface. An experimentally obtained scan of a line in a semiconductor integrated circuit with the tilted probe system is presented in FIG. 18. In this scan, the tip was first tilted in one direction, and afterwards in the other. The image is a patch of the images obtained in the left and right scans.

[0127] Carbon Nanotube Tips

[0128] Advanced semiconductor integrated circuit features with high aspect ratio are hard to inspect with conventional scanning probe tools that cannot reach vertical or near vertical sidewalls. This problem is well known to those of ordinary skills in the art. The embodiment of the present invention with a tilted probe solves this problem.

[0129] Another problem with conventional scanning probe tools is that conventional silicon tips have a hard time accessing the bottoms of aspect ratio trenches of advanced semiconductor integrated circuit features. This problem is well known to those of ordinary skills in the art. Conventional silicon tips have a half-cone angle of 20 to 30 degrees and are typically an integrated part of the silicon oscillator structure. The embodiment of the present invention with a tilted probe also has to deal with the feature access problem.

[0130] Therefore, to measure line-widths and trench-widths with high aspect ratios encountered with advanced semiconductor integrated circuit features, it is desirable to have a very sharp tip that can reach within the trench bottom and along vertical or reentrant sidewalls.

[0131] In one embodiment of the current invention, the standard oscillator tip is extended with an aligned nanotube tip grown from the apex of the sharp tip using the method of MANCEVSKI2, as shown in FIG. 19. Preferably, the nanotube is carbon nanotube. It is desirable to have a very sharp tip as a support structure on which a carbon nanotube tip extension is grown. Preferably, the sharp tip has a half-cone angle of 3 to 6 degrees.

[0132] In another embodiment of the present invention the support structure on which a carbon nanotube tip extension is grown is a column structure as depicted in FIG. 20. Column support structure is attached to an oscillator or cantilever and may be an integrated part of the oscillator structure. The current invention is not limited to this type of support structure. A nanotube tip extension or multiple nanotube tip extensions can be grown from the support. Nanotubes can be grown in accordance with the teaching of the issued U.S. Pat. No. 6,146,227 entitled “Method for Manufacturing Carbon Nanotubes as Functional Elements of MEMS Devices.” Carbon nanotube tip extensions that are simply attached or glued are less rigid, less stable, and provide less control over the position and orientation of the carbon nanotube tip extension, than ones that are grown in place using the method of MACEVSKI2.

[0133] A nanotube or multiple nanotubes may be oriented in any direction relative to the structure. However, FIG. 20 illustrates nanotubes oriented in lateral and vertical directions as to enable imaging of vertical and near vertical sidewalls and trench bottoms with a same nanotube tip extension.

[0134] Carbon Nanotube Oscillators

[0135] In yet another embodiment of the present invention, the tip is no longer a static rigid body that is used to transmit a surface force interaction to the elastic body of the oscillator, but it participates in the dynamics of the force sensing. In this embodiment, the tip is also an elastic body that is capable of oscillating in one or more resonant modes. Preferably, the elastic tip is a nanotube, or more specifically a carbon nanotube. We will refer to this elastic nanotube tip as nanotube oscillator, as shown in FIG. 21. The function of the nanotube oscillator is to serve as a force sensor.

[0136] Multiple resonant modes of the carbon nanotube oscillator can be used to provide sensitivity in at least one and preferably all three directions of the tip-sample force interaction. The nanotube oscillator force sensor embodiment of the present invention is consistent with all the capabilities and functions of the oscillator force sensor embodiment of our invention, and all discussion of the oscillator force sensor applies to the nanotube oscillator force sensor.

[0137] In the preferred nanotube oscillator force sensor embodiment of the present invention there is a column support structure vertically oriented with respect to the global coordinate system of the sample. Another type of support structure for the nanotube oscillator may be a rigid sharp tip. In the preferred embodiment there is a single carbon nanotube oriented vertically, as shown in FIG. 21. One resonance of interest is the second bending mode that will produce end-of-nanotube vibration that is vertical and therefore sensitive to the vertical Z component of the surface force vector. This resonant mode may have a projection in the XY plane that is in any direction. However, this is not relevant since the end- of-nanotube will move up and down in the vertical direction irrespective of the orientation of this mode.

[0138] Another resonance that can be used for force sensing is the first bending mode of the nanotube oscillator. Since the nanotube is a molecularly perfect cylindrical structure, there will be two first bending modes that have identical frequencies but produce end-of-nanotube vibrations that are normal to each other. Depending on the phase of the two bending resonant frequencies the end-of-nanotube vibration may be a diagonal or circular motion. Those two resonances are sensitive to the X and Y directions of the surface force interaction respectively. Although the resonant frequencies of the two modes are the same we may separate them by their phase and therefore make them useful for a feedback control, that is sensitive to the X and Y directions of the surface force interaction. In one of the embodiments of this invention we influence the phase of the two identical frequencies to be different by controlling the initial condition of the excitation. In another embodiment of this invention we attach a magnetic particle at the end of the nanotube to destroy the symmetry and produce distinguishing resonances with separated modes, as shown in FIG. 22. The magnetic particle may also be used to magnetically excite the nanotube oscillator. In another embodiment of this invention the grown nanotube has a shape that is not symmetrical to produce distinguishing resonances with separated modes.

[0139] Means of exciting the nanotube oscillator include:

[0140] 1) magnetic coupling to a magnetic particle attached at the end of the nanotube oscillator,

[0141] 2) coupling of electromagnetic radiation energy to the nanotube oscillator,

[0142] 3) electrostatic coupling to a charged particle attached at the end of the nanotube oscillator,

[0143] 4) thermal gradient near the nanotube oscillator,

[0144]5) piezoelectric element coupled to the support structure or the support structure may be a piezoelectric element,

[0145] 6) combination of any of the above means of excitation.

[0146] Means of detecting the vibrations of the nanotube oscillator include:

[0147] 1) magnetic coupling to a magnetic particle attached at the end of the nanotube oscillator,

[0148] 2) current readout from the nanotube oscillator that has been exposed to electromagnetic radiation or a stress,

[0149] 3) inductive pick-up coil and corresponding tank circuit,

[0150] 4) capacitive readout element positioned next to the nanotube oscillator that contains a charged particle attached at its end,

[0151] 5) an optical beam illumination and detection of its scattering,

[0152] 6) combination of any of the above means of detection.

[0153] In another embodiment of the nanotube oscillator force sensor embodiment of the present invention there is a column support structure vertically oriented with respect to the global coordinate system of the sample. In this embodiment there are more than one carbon nanotube, as depicted in FIG. 20, where each nanotube oscillator is responsible for detecting the component of the surface force vector in the direction in which it extends. Therefore, the vertically oriented nanotube oscillator is sensitive to vertical direction of the surface force interaction, and the horizontally (in X and Y) oriented nanotube oscillators are sensitive to the horizontal (X and Y) directions of the surface force interaction. In this embodiment it is sufficient that each nanotube oscillator utilize only one of its resonances since its orientation determines the direction of its sensitivity. Preferably, the single resonance of each nanotube oscillator is the second bending mode that will produce end-of-nanotube vibration that is oriented along its length and therefore it is sensitive to the direction of the surface force interaction that is oriented along the length of the nanotube.

[0154] Although the present invention has been described in detail, it should be understood that various changes, substitutions and alterations can be made hereto without departing from the spirit and scope of the invention as described by the appended claims.

[0155] It will be appreciated by those skilled in the art having the benefit of this disclosure that this invention provides SYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR SCANNING PROBE MICROSCOPY. It should be understood that the drawings and detailed description herein are to be regarded in an illustrative rather than a restrictive manner, and are not intended to limit the invention to the particular forms and examples disclosed. On the contrary, the invention includes any further modifications, changes, rearrangements, substitutions, alternatives, design choices, and embodiments apparent to those of ordinary skill in the art, without departing from the spirit and scope of this invention, as defined by the following claims. Thus, it is intended that the following claims be interpreted to embrace all such further modifications, changes, rearrangements, substitutions, alternatives, design choices, and embodiments. 

The invention claimed is:
 1. A multidimensional force sensor system for use in scanning probe microscopy, comprising: an oscillator having a rigid pointed tip extending therefrom, said oscillator having a means for being sensitive to surface force interactions between said tip and a sample surface in a first direction with a first resonance frequency, in a second direction with a second resonance frequency, and in a third direction with a third resonance frequency; a means for holding said probe structure and for positioning said tip and said sample relative to each other; a means for vibrating said probe structure at said first, second, and third resonance frequencies; a means for sensing said surface force interactions in said first, second, and third directions; a means for providing a first output based on said surface force interactions in said first direction; a means for providing a second output based on said surface force interactions in said second direction; a means for providing a third output based on said surface force interactions in said third direction; and a means for controlling said actuator based on said first, second, and third outputs. (Note to PTO examiner: More claims will be added in a preliminary amendment after filing due to time constraints in filing this continuation-in-part application.) 